In each question, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answers
I`2x^2-11x+15=0`
II `2y^2-17y+35=0`

Options

A. `xgty`
B. `xley`
C. `xlty`
D. `xgey`

Answer

To solve the given equations step by step, let's start with Equation I and then move on to Equation II.

### Step 1: Solve Equation I
The first equation is:
\[ 2x^2 - 11x + 15 = 0 \]

#### Step 1.1: Factor the quadratic
To factor the quadratic equation, we can look for two numbers that multiply to \(2 \times 15 = 30\) and add up to \(-11\). The numbers \(-6\) and \(-5\) fit this requirement.

So we can rewrite the equation as:
\[ 2x^2 - 6x - 5x + 15 = 0 \]

#### Step 1.2: Group the terms
Now, we group the terms:
\[ (2x^2 - 6x) + (-5x + 15) = 0 \]

#### Step 1.3: Factor by grouping
Factoring out the common terms:
\[ 2x(x - 3) - 5(x - 3) = 0 \]

Now we can factor out \((x - 3)\):
\[ (x - 3)(2x - 5) = 0 \]

#### Step 1.4: Solve for x
Setting each factor to zero gives us:
1. \(x - 3 = 0 \Rightarrow x = 3\)
2. \(2x - 5 = 0 \Rightarrow x = \frac{5}{2} = 2.5\)

So the solutions for \(x\) are:
\[ x = 3 \quad \text{and} \quad x = 2.5 \]

### Step 2: Solve Equation II
The second equation is:
\[ 2y^2 - 17y + 35 = 0 \]

#### Step 2.1: Factor the quadratic
We need to find two numbers that multiply to \(2 \times 35 = 70\) and add up to \(-17\). The numbers \(-7\) and \(-10\) work.

So we can rewrite the equation as:
\[ 2y^2 - 7y - 10y + 35 = 0 \]

#### Step 2.2: Group the terms
Now, we group the terms:
\[ (2y^2 - 7y) + (-10y + 35) = 0 \]

#### Step 2.3: Factor by grouping
Factoring out the common terms:
\[ y(2y - 7) - 5(2y - 7) = 0 \]

Now we can factor out \((2y - 7)\):
\[ (2y - 7)(y - 5) = 0 \]

#### Step 2.4: Solve for y
Setting each factor to zero gives us:
1. \(2y - 7 = 0 \Rightarrow y = \frac{7}{2} = 3.5\)
2. \(y - 5 = 0 \Rightarrow y = 5\)

So the solutions for \(y\) are:
\[ y = 3.5 \quad \text{and} \quad y = 5 \]

### Summary of Solutions
- The values of \(x\) are \(3\) and \(2.5\).
- The values of \(y\) are \(3.5\) and \(5\).

### Final Comparison
Now we compare the values:
- For \(x\): \(3\) and \(2.5\)
- For \(y\): \(3.5\) and \(5\)

Both values of \(y\) are greater than both values of \(x\):
- \(3.5 > 3\)
- \(5 > 2.5\)

Thus, the correct answer is:
**y > x**